Inferring network properties from time series via transfer entropy and mutual information: validation of bivariate versus multivariate approaches

Functional and effective networks inferred from time series are at the core of network neuroscience. Since it is common practice to compare network properties between patients and controls, it is crucial for inferred network models to reflect key underlying structural properties. However, even a few spurious links severely distort the shortest-path length and derived measures including the small-world coefficient, providing misleading insights into the macroscopic topology of the network. This poses a challenge for functional connectomes based on correlation, whose transitivity necessarily induce numerous false positives. We study how false positives bias the properties of the networks inferred by bivariate and multivariate algorithms. Mutual information, bivariate transfer entropy, and multivariate transfer entropy are respectively used for inferring functional, directed-functional, and effective networks. The validation is performed on synthetic ground truth networks with 100--200 nodes and various topologies (regular lattice, small-world, random, scale-free, modular), as well as on a real macaque connectome. The time series of node activity are simulated via autoregressive dynamics. We find that multivariate transfer entropy captures key properties of all network structures for longer time series. Bivariate methods can achieve higher recall (sensitivity) for shorter time series; however, as available data increases, they are unable to control false positives (lower specificity). This leads to overestimated clustering, small-world, and rich-club coefficients, underestimated shortest path lengths and hub centrality, and fattened degree distribution tails. Caution should therefore be used when interpreting network properties of functional connectomes obtained via correlation or pairwise statistical dependence measures, rather than more holistic (yet data-hungry) multivariate models.